This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309289 #24 Dec 23 2024 14:53:45 %S A309289 2,3,5,9,13,27,47,59,111,547,923,1301,2263,5189,45403,66901 %N A309289 Numbers k such that binomial(2k,k) - k^2 is prime. %C A309289 If a term k > 2 is divisible by a prime p, then all digits in the base-p expansion of k are less than p/2. In particular, 2 is the only even term. - _Robert Israel_, Aug 02 2019 %H A309289 Juri-Stepan Gerasimov and others, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2018-March/018478.html">C(2n,n) - n^2 and C(n^2,n) - n^n</a>, SeqFan list, April 20, 2018. %p A309289 filter:= t -> isprime(binomial(2*t,t)-t^2): %p A309289 select(filter, [2,seq(i,i=3..6000,2)]); # _Robert Israel_, Aug 02 2019 %o A309289 (PARI) is(n)=ispseudoprime(binomial(2*n,n)-n^2) %o A309289 for(n=0,oo, is(n) && print1(n,", ")) %Y A309289 Cf. A309290 (binomial(k^2,k) - k^2 is squarefree). %K A309289 nonn,hard,more %O A309289 1,1 %A A309289 _M. F. Hasler_ (at the suggestion of _Juri-Stepan Gerasimov_ and others), Jul 21 2019 %E A309289 a(15)-a(16) from _Michael S. Branicky_, Aug 24 2024